Exploring Linear Inequalities: Real-Life Applications

A car rental company charges a base fee of $30 plus $0.15 per mile driven. Write a linear inequality to represent the total cost (C) if a customer wants to spend no more than $60. Identify the slope and y-intercept.

• 30 + 0.15m ≤ 60; slope = 0.15, y-intercept = 30

• 30 + 0.10m ≤ 60; slope = 0.10, y-intercept = 30

• 30 + 0.15m ≥ 60; slope = 0.15, y-intercept = 30

• 20 + 0.15m ≤ 60; slope = 0.15, y-intercept = 20

A gym membership costs $25 per month plus a one-time registration fee of $50. Write a linear inequality to show the maximum number of months (m) a person can afford if they have a budget of $200. What is the slope and intercept?

• m <= 8; slope = -20, intercept = 50

• m <= 5; slope = -25, intercept = 100

• m <= 6; slope = -25, intercept = 50

• m <= 4; slope = -30, intercept = 50

A school is planning a field trip and has a budget of $500. The cost per student is $20. Write a linear inequality to represent the number of students (s) that can attend the trip. Identify the slope and y-intercept.

• 25s <= 500, slope: -25, y-intercept: 500

• 20s <= 500, slope: -20, y-intercept: 500

• 15s <= 500, slope: -15, y-intercept: 500

• 20s >= 500, slope: 20, y-intercept: 0

A local bakery sells cupcakes for $3 each. If they want to make at least $150 in sales, write a linear inequality to represent the number of cupcakes (c) they need to sell. What is the slope and intercept?

• 3c >= 150; slope: 0, intercept: 150

• 3c <= 150; slope: 0, intercept: 50

• c > 50; slope: 1, intercept: 150

• c < 50; slope: 3, intercept: 0

A phone plan costs $40 per month plus $0.10 per text message. If a customer wants to keep their monthly bill under $60, write a linear inequality for the number of text messages (t) they can send. Identify the slope and intercept.

• t < 150

• t < 100

• t < 200

• t < 250

A concert venue has a seating capacity of 500. If tickets are sold for $20 each, write a linear inequality to represent the total revenue (R) if they want to earn at least $8000. What is the slope and intercept?

• 10x >= 8000; slope = 10, intercept = 0

• 20x >= 10000; slope = 20, intercept = 500

• 20x >= 8000; slope = 20, intercept = 0

• 20x <= 8000; slope = 0, intercept = 20

A farmer sells apples for $2 per pound. If they want to earn at least $300, write a linear inequality to represent the number of pounds of apples (p) they need to sell. Identify the slope and intercept.

• p <= 150; slope: 1, intercept: 0

• 2p < 300; slope: 2, intercept: 300

• 2p >= 300; slope: 2, intercept: 0

• 3p >= 300; slope: 3, intercept: 0

Tags

CCSS.6.EE.B.8

A tutoring service charges $15 per hour. If a student has a budget of $120, write a linear inequality to represent the number of hours (h) they can afford. What is the slope and intercept?

• 15h ≤ 120; slope: -15, intercept: 120

• 15h ≥ 120; slope: 15, intercept: 0

• 20h ≤ 120; slope: -20, intercept: 120

• 10h ≤ 120; slope: -10, intercept: 120

A clothing store has a sale where each item costs $25. If a customer wants to spend no more than $200, write a linear inequality to represent the number of items (i) they can buy. Identify the slope and intercept.

• 25i ≤ 200, slope = 25, intercept = 200

• 25i < 200, slope = 1, intercept = 25

• 25i ≥ 200, slope = 50, intercept = 0

• 25i = 200, slope = 0, intercept = 25